Part-7 Waves Hard

An unknown fork produces 4 beats per second with a tuning fork of frequency 288 Hz. When unknown fork is loaded with wax it again produces 4 beats per second. The unknown frequency of tuning fork is -

Consider a plane standing sound wave of frequency 10³ Hz in air at 300 K. Suppose the amplitude of pressure variation associated with this wave is 1 dyne/cm². The equilibrium pressure is 10⁶ dyne/cm². The amplitude of displacement of air molecules associated with this wave is :

(Given speed of sound : 340 m/s

Molar mass of air : 29 × 10^–3 kg/mol)

Two closed end pipes when sounded together produce 5 beat per second. If their length are in the ratio 100 : 101, then fundamental notes produced by them are –

A wave is represented by y = A sin² (kx – ωt + Φ). The amplitude and wavelength of wave is given by -

Four waves are represented by y₁ = A₁ sin πt,

y₂ = A₂ sin (πt + π/2), y₃ = A₁ sin (2πt + π/2) and y₄ = A₂ sin (πt – π/3). Interference will happen with –

Intensity and phase of three sound wave reaching at some point in space is I₀, 4 I₀, I₀ and 10⁰, 130⁰ and 250⁰ Resultant intensity at that point will be –

Three sound waves of equal amplitudes have frequencies (v – 1), v, (v + 1). They superpose to give beats. The number of beats produced per second will be –

An organ pipe open at one end is vibrating in first overtone and is in resonance with another pipe open at both ends and vibrating in third harmonic. The ratio of length of two pipes is

A piezo electric quartz crystal of thickness 0.005 m is vibrating in resonate conditions. Calculate the fundamental frequency f₀ for quartz

Y = 8 × 10¹⁰Nm^–2 and r = 2.65 × 10³ kgm^–3

Two perfectly identical wires kept under tension are in unison. When the tension in wire is increased by 1% then on sounding them together 3 beats are heard in 2 seconds. Find the frequency of each wire -

In a mixture of gases, the average number of degrees of freedom per molecule is 6. The rms speed of the molecules of the gas is c. The velocity of sound in the gas is -

A wave equation which gives the displacement along Y-direction is given :

y = 10^–4 sin (60t + 2x).

where x and y are in metre and t in sec. Among the following choose the correct statement :

Two waves are propagating to the point P along a straight line produced by two sources A and B of simple harmonic and of equal frequency. The amplitude of every wave at P is 'a' and the phase of A is ahead by π/3 than that of B and the distance AP is greater than BP by 50 cm. Then the resultant amplitude at the point P will be, if the wavelength is 1 meter -

Equation of motion in the same direction is given by y₁ = A sin(ωt – kx), y₂ = A sin(ωt – kx – θ). The amplitude of the medium particle will be -

207. Two waves having equations

x₁ = a sin(ωt + Φ₁), x₂ = a sin(ωt + Φ)

If in the resultant wave the frequency and amplitude remain equal to those of superimposing waves. Then phase difference between them is -